标题： 使用微积分网络动力学保证和解释异构负载均衡的稳定性 显示英文标题

标题： Guaranteeing and Explaining Stability across Heterogeneous Load Balancing using Calculus Network Dynamics

摘要： 在基站（BS）之间进行负载均衡可以高效利用BS容量并避免中断。目前，数据驱动的机制旨在平衡基站间的负载并减少不必要的切换。挑战在于，在大量基站的情况下，网络观察到负载演化的振荡效应，这会导致高频率的基站间消息传递。如果没有一种将网络拓扑整合进来的微积分函数来描述负载状态的演化，当前的数据驱动算法无法解释在负载状态中观察到的振荡现象，也无法提供对理想同步状态稳定性的理论保证。尽管我们知道负载状态的振荡与负载均衡过程算法和基站间边界关系的拓扑结构有关，但我们缺乏一个理论框架来证明这一点，并且没有改进负载均衡算法的途径。在这里，我们将通用和异构的数据驱动算法抽象为一个微积分动力学空间，以便我们可以建立具有任何网络拓扑的网络负载均衡动力学的同步条件。通过引入所谓的“非保守误差”和网络动力学的特征值谱，我们可以调整基站间的负载均衡机制，以实现高效率和收敛性保证，或者在同步条件无法满足时减轻振荡。 显示英文摘要

摘要： Load balancing between base stations (BSs) allows BS capacity to be efficiently utilised and avoid outages. Currently, data-driven mechanisms strive to balance inter-BS load and reduce unnecessary handovers. The challenge is that over a large number of BSs, networks observe an oscillatory effect of load evolution that causes high inter-BS messaging. Without a calculus function that integrates network topology to describe the evolution of load states, current data-driven algorithms cannot explain the oscillation phenomenon observed in load states, nor can they provide theoretical guarantees on the stability of the ideal synchronised state. Whilst we know load state oscillation is coupled with the load balancing process algorithms and the topology structure of inter-BS boundary relations, we do not have a theoretical framework to prove this and a pathway to improving load balancing algorithms. Here, we abstract generic and heterogeneous data-driven algorithms into a calculus dynamics space, so that we can establish the synchronization conditions for networked load balancing dynamics with any network topology. By incorporating what is known as "non-conservative error" and the eigenvalue spectrum of the networked dynamics, we can adjust the inter-BS load balancing mechanisms to achieve high efficiency and convergence guarantee, or to mitigate the oscillation when the synchronisation condition cannot be satisfied.